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Author, Editor

Author(s):

Emiris, Ioannis
Hemmer, Michael
Tsigaridas, Elias
Tzoumas, Georg

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Not MPG Author(s):

Emiris, Ioannis
Tsigaridas, Elias
Tzoumas, Georg

Editor(s):





BibTeX Citekey*:

ACS-TR-363603-01

Language:

English

Title, Institution

Title*:

Voronoi diagram of ellipses: CGAL-based implementation

Institution*:

University of Groningen

Publishers or Institutions Address*:

9700 AB Groningen THE NETHERLANDS

Type:

Technical Report

No, Year, pp.,

Number*:

ACS-TR-363603-01

Pages*:

18

Month:

April

VG Wort
Pages*:

14

Year*:

2008

ISBN/ISSN:






DOI:




Note, Abstract, ©

Note:


(LaTeX) Abstract:

We present a C++ open-source implementation of an incremental algorithm
for the computation of the Voronoi diagram of ellipses in the Euclidean
plane. This is the first complete implementation, under the exact computation
paradigm; it also computes the approximate diagram with any given precision.
It is based on the cgal package for the Apollonius diagram. The ellipses
are given in parametric representation, which allows us to develop a GUI for
input / output. The software concerns non-intersecting ellipses, but it can be
generalized. We implement an interval Newton solver, bivariate polynomial
interpolation, and trivariate system resultant computation, and demonstrate
the factorization of certain resultants so as to arrive at an efficient implementation
of InCircle . As a ballmark estimate, our code spends about 99sec
to construct the Voronoi diagram of 128 ellipses, when few degeneracies occur.
It is faster than the cgal Voronoi diagram of polygons, when ellipses
are approximated by k-gons for k > 15, but expectedly slower on circles than
the cgal Apollonius package. Our software is connected to the algebraic library
Synaps and, through it, to libraries mpfr and ntl, hence illustrating
the concept of algebraic support for geometric computing; it is targeted for
inclusion in the cgal library. In this direction, we present some experiments
using the new Algebraic Kernel from MPI.

Categories / Keywords:

Exact Geometric Computing, CGAL, Generic Programming, Voronoi Diagrams

Copyright Message:


HyperLinks / References / URLs:

http://acs.cs.rug.nl/acstr/ACS-TR-363603-01.pdf

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Access Level:

Public

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Algorithms and Complexity Group

Audience:

experts only

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort


BibTeX Entry:
@TECHREPORT{ACS-TR-363603-01,
AUTHOR = {Emiris, Ioannis and Hemmer, Michael and Tsigaridas, Elias and Tzoumas, Georg},
TITLE = {Voronoi diagram of ellipses: CGAL-based implementation},
YEAR = {2008},
TYPE = {Technical Report},
INSTITUTION = {University of Groningen},
NUMBER = {ACS-TR-363603-01},
PAGES = {18},
ADDRESS = {9700 AB Groningen THE NETHERLANDS},
MONTH = {April},
}


Entry last modified by Michael Hemmer, 03/03/2009
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Editor(s)
Michael Hemmer
Created
01/26/2009 02:43:57 PM
Revision
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Editor
Michael Hemmer



Edit Date
01/26/2009 02:43:57 PM



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